The musician, 72, lost his voice mid-way through his set at Auckland's Mount Smart Stadium on Sunday.
"I've just completely lost my voice. I can't sing," Sir Elton told the crowd. "I've got to go. I'm sorry."
Sir Elton appeared to break down in tears as he leaned on his piano and shook his head.
The audience gave the English singer a rapturous ovation as he walked gingerly off stage, helped by several assistants.
Earlier in his set, Sir Elton told the sold-out crowd he had been diagnosed with walking pneumonia on Sunday.
The concert was one of a number of New Zealand shows on Sir Elton's Farewell Yellow Brick Road tour.
Walking pneumonia, also called atypical pneumonia, is a type of lung infection often caused by bacteria or viruses.
It is less severe than other types of pneumonia, with most sufferers not requiring medical attention. Symptoms are comparable to those of a bad cold, often including a cough, chest pain, a sore throat and a headache.
Sir Elton was checked by a medic halfway through the show and, despite his illness, was able to perform classics such as Candle in the Wind and All the Girls Love Alice.
But ultimately, he was unable to finish the set, his voice giving way as he attempted to sing Daniel.
Shortly after leaving the stage, Sir Elton apologised to his fans in an emotional Instagram post.
"I played and sang my heart out, until my voice could sing no more. I'm disappointed, deeply upset and sorry. I gave it all I had. Thank you so much for your extraordinary support and all the love you showed me during tonight's performance. I am eternally grateful. Love, Elton xx," he wrote.
On social media, concertgoers expressed sympathy for the singer, who remains one of the world's most in-demand live performers.
Sir Elton John announced in 2018 that he would stop touring in order to prioritise his family. But he announced he would say goodbye to fans with a series of 300 dates spanning three years.
It is not clear what effect Sir Elton's illness will have on upcoming tour dates.
The star is scheduled to play two more concerts in Auckland on Tuesday and Thursday as part of the tour.